1. Genetic Algorithms: An Overview

학습목표

GA 의 기본원리를 파악하고 , Prisoner’s dilemma 와sorting network 에의 응용 및 이론적 배경을

이해한다

Outline

Brief history of EC Appeal of evolution Biological terminology Search space and fitness landscape Elements of GA Simple GA GA and traditional search methods Some applications of GAs Two brief examples How do GAs work?

GA: An Overview

EAs can be regarded as population-based, stochastic generate-and-test algorithms

Two issuesHow to generate offspring?How to test (select) them?

EAs represent a whole family of algorithms, with different representation, search operators, etc EC covers at least four major areas EC is closely related to AI, CS, Operations Research, Machine Learning, Engineering, etc

Brief History

Rechenberg (1965, 1973): evolution strategies Schwefel (1975, 1977)

Fogel, Owens & Walsh (1966): evolutionary programming John Holland: GA

chromosomes natural selection genes & allele (0 or 1) crossover/recombination with haploid schema

Appeal of Evolution

Searching through a huge number of possibilities for solutions computational protein engineering, financial market

A computer program to be adaptive bottom-up paradigm: emergence of intelligence

Designing innovative solutions to complex problems immune systems

Rules of evolution is simple species evolve by means of random variation, followed by natural selection where the fittest tend to survive and reproduce

Biological Terminology

chromosomes(strings of DNA): blueprint for the organism a gene encodes a trait (eye color, …) alleles: possible settings for a trait (blue, brown, …)

genome: multiple chromosomes in a cell genotype: particular set of genes phenotype: its physical & mental characteristics

diploid vs haploid

Search Spaces & Fitness Landscapes

search space some collection of candidate solutions to a problem and some notion of distance between candidate solutions

fitness landscape a representation of the space of all possible genotypes along with their fitnesses hill, peak, valley

Elements of GAs

Fitness function GA operators

selection crossover mutation

Simple GA: Generate-and-Test

LoopGenerate a candidate solutionTest the candidate solution

Until a satisfactory solution is found or no more candidate solutions can be found

…

Generator TesterCandidateSolutions

GA and Traditional Search Methods

Search for stored data Search for paths to goals Search for solutions

Some Applications of GAs

Optimization Automatic programming Machine learning Economics Immune systems Ecology Population genetics Evolution and learning Social systems

Homework 1

Prisoner’s dilemma 문제의 해결을 위한 EC 방법을 인코딩 , 오퍼레이터 , 결과에 대해 조사하시오 .

Sorting network 문제의 해결을 위한 EC 방법을 인코딩 , 오퍼레이터 , 결과에 대해 조사하시오 .

Iterated Prisoner’s Dilemma (1)

Non-zero sum, non-cooperative gamesThe 2 player version

The purpose here is not to find the optimal solution for some simplified conditions, but to study how to find itFitness evaluation

Entirely determined by the total payoff obtained through playing against each otherThe initial population was generated at random

Player A

Player B

C DC

D

33

11

00

5

5

Iterated Prisoner’s Dilemma (2)

Representation of strategies

History Table Recent Action ∙∙∙ Last Action Recent Action ∙∙∙ Last Action

Own History Opponent’s History

0 1 0 ∙∙∙ 1

l = 2 : Example History 11 01

2N History

Iterated Prisoner’s Dilemma (3)

Test strategies

Strategy CharacteristicsTit-For-Tat Initially cooperate, and then follow opponent

Trigger Initially cooperate. Once opponent defects, continuously defect

AllD Always defectCDCD Cooperate and defect over and overCCD Cooperate and cooperate and defectRandom Random move

Example Strategies

0 0 1 0 1 1 0 0

0 0 0 1 1 1 1 1

1 1 1 1 1 1 1 1

0 1 0 1 0 1 0 1

0 0 1 0 0 1 0 0

1 1 0 1 0 0 1 1

Tit-for-Tat

Trigger

AllD

CDCD

CCD

Random

Sorting Networks (1)

A sorting algorithm in essence, but can be represented graphically for the ease of understanding Used widely in switching circuits, routing algorithms, and other areas in interconnection networks Two issues

Number of comparators Number of layers

Best known networks with 16 inputs

Year 1962 1964 1969 1969

Designers Bose, Nelson Batcher, Knuth Shapiro Green

# comparators 65 63 62 60

still the best known today

Sorting Networks (2)Comparators

Graphical representation of a sorting network

unsortedinput

sortedoutput

small

large

inputelement

unsortedinput

sortedoutput

a layer

How do GAs Work? (1)Traditional assumption

GA works by discovering, emphasizing, and recombining good “building blocks” of solutions in a highly parallel fashion

Schemas = building blocksA set of bit strings that can be described by a template made up of ones, zeros, and asterisks (don’t cares)Instance of H: strings fit the template HOrder: defined bits (non-asterisks) in a HDefining length: distance between its outermost defined bits

How does GA process schemas?A bit string of length l = an instance of 2^l different schemasNo. of schema instances in a population of n strings

2^l ~ n*2^l

How do GAs Work? (2)Schema Theorem

P. 29: equation (1.2) lower bound in destructive effects of crossover and mutationDesription: Growth of a schema from one generation to the nextImplication: Short, low-order schemas whose average fitness remains above the mean will receive exponentially increasing numbers of samples over timeReason: no. of samples of those schemas that are not disrupted and remain above average in fitness increases by a factor of U/F at each generation